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10th Class Mathematics Probability Question Bank Case Based (MCQs) - Probability

  • question_answer
    Study Case : Q. 36 to 40
    Sanjeev is very found of collecting balls of different colours. He has a total of 25 balls in his basket out of which five balls are red in colour and eight are white. Out of the remaining balls, some are green in  colour and the rest are pink:            
     
    if the probability of drawing a pink ball is twice the probability of drawing a green ball, then the number of pink balls is:

    A) 4

    B) 8

    C) 10

    D) 12

    Correct Answer: B

    Solution :

    [b] As the total number of balls is 25 and number of red balls + white balls is 12.
    \[\therefore \] Total number of green balls + pink balls \[=\text{25}-\text{13}=\text{12}\]
    Let the number of pink balls be x.
    Then the number of green balls\[=\text{12}-\text{x}\].
    We know. Probability of an event E is given by
    \[P(E)=\frac{\text{Number of outcomes favrouable E}}{\text{Total Number of possible outcomes}}\]
    \[\therefore \] Probability of drawing a pink ball \[=\frac{x}{25}\] and probability of drawing a green ball \[=\frac{12-x}{25}.\]
    It is given that
    \[\text{P(pink ball})=\text{2}\times \text{P(green ball})\].
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{x}{25}=2\times \left( \frac{12-x}{25} \right)\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=24-2x\,\,\Rightarrow \,\,3x=24\,\,\Rightarrow \,\,x=8\]
    Therefore, number of pink balls = 8.


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